-(4-2)-in-slope-intercept-form.jpeg "(0 3) (4 2) In Slope Intercept Form")
Understanding the Slope-Intercept Form of a Linear Equation
The slope-intercept form of a linear equation is a fundamental concept in algebra and geometry. It's a way to express a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
In this article, we'll explore how to convert the equation (0, 3) (4, 2) into the slope-intercept form.
What is the Slope-Intercept Form?
The slope-intercept form of a linear equation is written as:
y = mx + b
Where:
- m is the slope (a measure of how steep the line is)
- b is the y-intercept (the point where the line crosses the y-axis)
Converting the Equation (0, 3) (4, 2) to Slope-Intercept Form
The equation (0, 3) (4, 2) represents two points on a line. To convert this equation to slope-intercept form, we need to find the slope m and the y-intercept b.
Step 1: Find the Slope (m)
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) = (0, 3) and (x2, y2) = (4, 2)
m = (2 - 3) / (4 - 0) m = -1 / 4 m = -0.25
Step 2: Find the Y-Intercept (b)
Now that we have the slope, we can use one of the points to find the y-intercept. Let's use the point (0, 3).
y = mx + b 3 = -0.25(0) + b 3 = b
So, the y-intercept is b = 3.
The Slope-Intercept Form of the Equation
Now that we have the slope m and the y-intercept b, we can write the equation in slope-intercept form:
y = -0.25x + 3
This is the slope-intercept form of the equation (0, 3) (4, 2).
Conclusion
In this article, we've seen how to convert the equation (0, 3) (4, 2) to slope-intercept form. By finding the slope and y-intercept, we can express the equation in the form y = mx + b, making it easier to graph and analyze the line.
